Study of Markowitz Model with an Example Under Portfolio Management

MARKOWITZ MODEL WITH AN EXAMPLE

To choose the best portfolio from a number of possible portfolios, each with different return and risk, two separate decisions are to be made :

1. Determination a set of efficient portfolios.

2. Selection of best portfolio out of the efficient set.

Determining the Efficient Set

A portfolio that gives maximum return for a given risk, or minimum risk for given return is an efficient portfolio. Thus, portfolios are selected as follows:

(a) From the portfolios that have the same return, the investor will prefer the portfolio with lower risk, and [6]

(b) From the portfolios that have the same risk level, an investor will prefer the portfolio with higher rate of return.

Figure 1: Risk-Return of Possible Portfolios

As the investor is rational, they would like to have higher return. And as he is risk averse, he wants to have lower risk.[6] In Figure 1, the shaded area PVWP includes all the possible securities an investor can invest in. The efficient portfolios are the ones that lie on the boundary of PQVW. For example, at risk level x2, there are three portfolios S, T, U. But portfolio S is called the efficient portfolio as it has the highest return, y2, compared to T and U. All the portfolios that lie on the boundary of PQVW are efficient portfolios for a given risk level.

The boundary PQVW is called the Efficient Frontier. All portfolios that lie below the Efficient Frontier are not good enough because the return would be lower for the given risk. Portfolios that lie to the right of the Efficient Frontier would not be good enough, as there is higher risk for a given rate of return. All portfolios lying on the boundary of PQVW are called Efficient Portfolios. The Efficient Frontier is the same for all investors, as all investors want maximum return with the lowest possible risk and they are risk averse.

Choosing the best Portfolio

For selection of the optimal portfolio or the best portfolio, the risk-return preferences...